Advanced Neural Networks

Joaquin Vanschoren, Eindhoven University of Technology

Overview

• Convolutional neural networks
• Data augmentation
• Using pre-trained networks
• Batch normalization

SVHN = oml.datasets.get_dataset(41081)
X, y, cats, attrs = SVHN.get_data(dataset_format='array',
    target=SVHN.default_target_attribute)

Some lessons from Assignment 1

• We saw that greyscaling the image helps, but not a lot
• Problem: numbers can be dark on a light background, or vice versa
  • We care about where the boundaries are, not the exact pixel values
• Problem: the location within the image matters, but not exactly
  • We care about the center, but not exactly where in the center
• In short, we care about shapes (relationships between nearby pixels) much more than the actual pixel values

from random import randint
def rgb2gray(X, dim=32):
    return np.expand_dims(np.dot(X.reshape(len(X), dim*dim, 3), [0.2990, 0.5870, 0.1140]), axis=3)
Xsm = rgb2gray(X[:100])

def plot_images(X, y, grayscale=False):
    fig, axes = plt.subplots(1, len(X),  figsize=(10, 5))
    for n in range(len(X)):
        if grayscale:
            axes[n].imshow(X[n].reshape(32, 32)/255, cmap='gray')
        else:
            axes[n].imshow(X[n].reshape(32, 32, 3)/255)
        axes[n].set_xlabel((y[n]+1)) # Label is index+1
        axes[n].set_xticks(()), axes[n].set_yticks(())
    plt.show();

images = range(5)
X_random = [Xsm[i] for i in images]
y_random = [y[i] for i in images]
plot_images(X_random, y_random, grayscale=True)
sv3 = X_random[3]

Convolutional neural nets

• When processing image data, we want to discover 'local' patterns (between nearby pixels)
  • edges, lines, structures
• Consider windows (or patches) of pixels (e.g 5x5)

Convolution

• Slide an $n$ x $n$ filter (or kernel) over $n$ x $n$ patches of the input feature map
• Replace pixel values with the convolution of the kernel with the underlying image patch

• The convolution operation itself takes the sum of the values of the element-wise product of the image patch with the kernel

def apply_kernel(center, kernel, orig_image):
    image_patch = orig_image[window_slice(center, kernel)]
    # An element-wise multiplication followed by the sum
    return np.sum(kernel * image_patch)

• Different kernels can detect different types of patterns in the image

horizontal_edge_kernel = np.array([[ 1,  2,  1],
                                   [ 0,  0,  0],
                                   [-1, -2, -1]])
diagonal_edge_kernel = np.array([[1, 0, 0],
                                 [0, 1, 0],
                                 [0, 0, 1]])
edge_detect_kernel = np.array([[-1, -1, -1],
                               [-1,  8, -1],
                               [-1, -1, -1]])

plt.subplot(1, 3, 1)
plt.title("Horizontal edge kernel")
plt.imshow(horizontal_edge_kernel, cmap='gray_r')
plt.subplot(1, 3, 2)
plt.title("Diagonal edge kernel")
plt.imshow(diagonal_edge_kernel, cmap='gray_r')
plt.subplot(1, 3, 3)
plt.title("Edge detect kernel")
plt.imshow(edge_detect_kernel, cmap='gray_r')
plt.tight_layout();

Demonstration: horizontal edge filter

• Responds only to horizontal edges, sensitive to the 'direction' of the edge

# Simple image, just a white box
bright_square = np.zeros((10, 10), dtype=float)
bright_square[2:8, 2:8] = 1

titles = ('Image and kernel', 'Filtered image')
demo = convolution_demo(bright_square, horizontal_edge_kernel,
                        vmin=-4, vmax=4, titles=titles, cmap='gray_r')

demo(i_step=99)

Let's do this for a streetview image

image = sv3.reshape((32, 32))
image = (image - np.min(image))/np.ptp(image) # Normalize
imgplot=plt.imshow(image, cmap='gray_r')

Demonstration: horizontal edge filter

demo2 = convolution_demo(image, horizontal_edge_kernel,
                 vmin=-4, vmax=4, cmap='gray_r');

demo2(i_step=1023)

MNIST Demonstration: diagonal edge filter

demo3 = convolution_demo(image, diagonal_edge_kernel,
                 vmin=-4, vmax=4, cmap='gray_r');

demo3(i_step=1023)

MNIST Demonstration: edge detect filter

demo4 = convolution_demo(image, edge_detect_kernel,
                 vmin=-4, vmax=4, cmap='gray_r');

demo4(i_step=1023)

Image convolution in practice

• Convolutions have always been used to preprocess image data
• Families of kernels were run on every image (e.g. Gabor filters)

from scipy import ndimage as ndi
from skimage import data
from skimage.util import img_as_float
from skimage.filters import gabor_kernel

# Gabor Filters.
@interact
def demoGabor(frequency=(0.01,1,0.05), theta=(0,3.14,0.1), sigma=(0,5,0.1)):
    plt.gray()
    plt.imshow(np.real(gabor_kernel(frequency=frequency, theta=theta, sigma_x=sigma, sigma_y=sigma)), interpolation='nearest')

demoGabor(frequency=0.86, theta=1.9, sigma=1.7)

### Gabor filters applied to Fashion-MNIST example
### Just for illustration. Can be removed in the final submission.
### Careful, it takes a few seconds to do the convolution
# Calculate the magnitude of the Gabor filter response given a kernel and an imput image
def magnitude(image, kernel):
    image = (image - image.mean()) / image.std() # Normalize images
    return np.sqrt(ndi.convolve(image, np.real(kernel), mode='wrap')**2 +
                   ndi.convolve(image, np.imag(kernel), mode='wrap')**2)

Demonstration on the streetview data

@interact
def demoGabor2(frequency=(0.01,1,0.05), theta=(0,3.14,0.1), sigma=(0,5,0.1)):
    plt.subplot(131)
    plt.title('Original')
    plt.imshow(image)
    plt.subplot(132)
    plt.title('Gabor kernel')
    plt.imshow(np.real(gabor_kernel(frequency=frequency, theta=theta, sigma_x=sigma, sigma_y=sigma)), interpolation='nearest')
    plt.subplot(133)
    plt.title('Response magnitude')
    plt.imshow(np.real(magnitude(image, gabor_kernel(frequency=frequency, theta=theta, sigma_x=sigma, sigma_y=sigma))), interpolation='nearest')

demoGabor2(frequency=0.96, theta=1.7, sigma=0.3)

• It also works for general images
• Toy example: Fashion-MNIST

# build a list of figures for plotting
def buildFigureList(fig, subfiglist, titles, length):
    for i in range(0,length):
        pixels = np.array(subfiglist[i], dtype='float')
        pixels = pixels.reshape((28, 28))
        a=fig.add_subplot(1,length,i+1)
        imgplot =plt.imshow(pixels, cmap='gray_r')
        a.set_title(titles[i], fontsize=6)
        a.axes.get_xaxis().set_visible(False)
        a.axes.get_yaxis().set_visible(False)
    return

subfiglist = []
titles=[]

for i in range(0,10):
    subfiglist.append(X[i])
    titles.append(i)

buildFigureList(plt.figure(1),subfiglist, titles, 10)
plt.show()

boot = X[0].reshape((28, 28))

Demonstration: Fashion MNIST

image=boot
@interact
def demoGabor2(frequency=(0.01,1,0.05), theta=(0,3.14,0.1), sigma=(0,5,0.1)):
    plt.subplot(131)
    plt.title('Original')
    plt.imshow(image)
    plt.subplot(132)
    plt.title('Gabor kernel')
    plt.imshow(np.real(gabor_kernel(frequency=frequency, theta=theta, sigma_x=sigma, sigma_y=sigma)), interpolation='nearest')
    plt.subplot(133)
    plt.title('Response magnitude')
    plt.imshow(np.real(magnitude(image, gabor_kernel(frequency=frequency, theta=theta, sigma_x=sigma, sigma_y=sigma))), interpolation='nearest')

demoGabor2(frequency=0.81, theta=2.7, sigma=0.9)

Fashion MNIST with multiple filters (filter bank)

# Fetch some Fashion-MNIST images
boot = X[0].reshape(28, 28)
shirt = X[1].reshape(28, 28)
dress = X[2].reshape(28, 28)
image_names = ('boot', 'shirt', 'dress')
images = (boot, shirt, dress)

plt.rcParams['figure.dpi'] = 80

# Create a set of kernels, apply them to each image, store the results
results = []
kernel_params = []
for theta in (0, 1):
    theta = theta / 4. * np.pi
    for frequency in (0.1, 0.4):
        for sigma in (1, 3):
            kernel = gabor_kernel(frequency, theta=theta,sigma_x=sigma,sigma_y=sigma)
            params = 'theta=%.2f,\nfrequency=%.2f\nsigma=%.2f' % (theta, frequency, sigma)
            kernel_params.append(params)
            results.append((kernel, [magnitude(img, kernel) for img in images]))

# Plotting
fig, axes = plt.subplots(nrows=9, ncols=4, figsize=(6, 12))
plt.gray()
#fig.suptitle('Image responses for Gabor filter kernels', fontsize=12)
axes[0][0].axis('off')

# Plot original images
for label, img, ax in zip(image_names, images, axes[0][1:]):
    ax.imshow(img)
    ax.set_title(label, fontsize=9)
    ax.axis('off')

for label, (kernel, magnitudes), ax_row in zip(kernel_params, results, axes[1:]):
    # Plot Gabor kernel
    ax = ax_row[0]
    ax.imshow(np.real(kernel), interpolation='nearest') # Plot kernel
    ax.set_ylabel(label, fontsize=7)
    ax.set_xticks([]) # Remove axis ticks 
    ax.set_yticks([])

    # Plot Gabor responses with the contrast normalized for each filter
    vmin = np.min(magnitudes)
    vmax = np.max(magnitudes)
    for patch, ax in zip(magnitudes, ax_row[1:]):
        ax.imshow(patch, vmin=vmin, vmax=vmax) # Plot convolutions
        ax.axis('off')

plt.show();

plt.rcParams['figure.dpi'] = 120

Convolutional layers: Feature maps

• We slide $d$ filters across the input image in parallel, producing a (1x1xd) output per patch, reassembled into the final feature map with $d$ 'channels', a (width x height x d) tensor.
• The filters are randomly initialized, we want to learn the optimal values for the input data

Border effects

• Consider a 5x5 image and a 3x3 filter: there are only 9 possible locations, hence the output is a 3x3 feature map
• If we want to maintain the image size, we use zero-padding, adding 0's all around the input tensor.

Undersampling

• Sometimes, we want to downsample a high-resolution image
  • Faster processing, less noisy (hence less overfitting)
• One approach is to skip values during the convolution
  • Distance between 2 windows: stride length
• Example with stride length 2 (without padding):

Max-pooling

• Another approach to shrink the input tensors is max-pooling:
  • Run a filter with a fixed stride length over the image
    • Usually 2x2 filters and stride lenght 2
  • The filter returns the max (or avg) of all values
• Agressively reduces the number of weights (less overfitting)
• Information from every input node spreads more quickly to output nodes
  • In pure convnets, one input value spreads to 3x3 nodes of the first layer, 5x5 nodes of the second, etc.
  • You'd need much deeper networks, which are much harder to train

Convolutional nets in practice

• Let's model MNIST again, this time using convnets
• Conv2D for 2D convolutional layers
  • Default: 32 filters, randomly initialized (from uniform distribution)
• MaxPooling2D for max-pooling
  • 2x2 pooling reduces the number of inputs by a factor 4

model = models.Sequential()
model.add(layers.Conv2D(32, (3, 3), activation='relu', 
                        input_shape=(28, 28, 1)))
model.add(layers.MaxPooling2D((2, 2)))
model.add(layers.Conv2D(64, (3, 3), activation='relu'))
model.add(layers.MaxPooling2D((2, 2)))
model.add(layers.Conv2D(64, (3, 3), activation='relu'))

Observe how the input image is reduced to a 3x3x64 feature map

model.summary()

Model: "sequential_1"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
conv2d_1 (Conv2D)            (None, 26, 26, 32)        320       
_________________________________________________________________
max_pooling2d_1 (MaxPooling2 (None, 13, 13, 32)        0         
_________________________________________________________________
conv2d_2 (Conv2D)            (None, 11, 11, 64)        18496     
_________________________________________________________________
max_pooling2d_2 (MaxPooling2 (None, 5, 5, 64)          0         
_________________________________________________________________
conv2d_3 (Conv2D)            (None, 3, 3, 64)          36928     
=================================================================
Total params: 55,744
Trainable params: 55,744
Non-trainable params: 0
_________________________________________________________________

Compare to the architecture without max-pooling:

• Output layer is a 22x22x64 feature map!

model_no_max_pool = models.Sequential()
model_no_max_pool.add(layers.Conv2D(32, (3, 3), activation='relu',
                      input_shape=(28, 28, 1)))
model_no_max_pool.add(layers.Conv2D(64, (3, 3), activation='relu'))
model_no_max_pool.add(layers.Conv2D(64, (3, 3), activation='relu'))
model_no_max_pool.summary()

Model: "sequential_2"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
conv2d_4 (Conv2D)            (None, 26, 26, 32)        320       
_________________________________________________________________
conv2d_5 (Conv2D)            (None, 24, 24, 64)        18496     
_________________________________________________________________
conv2d_6 (Conv2D)            (None, 22, 22, 64)        36928     
=================================================================
Total params: 55,744
Trainable params: 55,744
Non-trainable params: 0
_________________________________________________________________

• To classify the images, we still need a Dense and Softmax layer.
• We need to flatten the 3x3x36 feature map to a vector of size 576

model.add(layers.Flatten())
model.add(layers.Dense(64, activation='relu'))
model.add(layers.Dense(10, activation='softmax'))

model.summary()

Model: "sequential_1"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
conv2d_1 (Conv2D)            (None, 26, 26, 32)        320       
_________________________________________________________________
max_pooling2d_1 (MaxPooling2 (None, 13, 13, 32)        0         
_________________________________________________________________
conv2d_2 (Conv2D)            (None, 11, 11, 64)        18496     
_________________________________________________________________
max_pooling2d_2 (MaxPooling2 (None, 5, 5, 64)          0         
_________________________________________________________________
conv2d_3 (Conv2D)            (None, 3, 3, 64)          36928     
_________________________________________________________________
flatten_1 (Flatten)          (None, 576)               0         
_________________________________________________________________
dense_1 (Dense)              (None, 64)                36928     
_________________________________________________________________
dense_2 (Dense)              (None, 10)                650       
=================================================================
Total params: 93,322
Trainable params: 93,322
Non-trainable params: 0
_________________________________________________________________

• Train and test as usual (takes about 5 minutes):
• Compare to the 97,8% accuracy of the earlier dense architecture

model.compile(optimizer='rmsprop',
              loss='categorical_crossentropy',
              metrics=['accuracy'])
model.fit(train_images, train_labels, epochs=5, batch_size=64)
test_loss, test_acc = model.evaluate(test_images, test_labels)

model.compile(optimizer='rmsprop',
              loss='categorical_crossentropy',
              metrics=['accuracy'])
model.fit(train_images, train_labels, epochs=5, batch_size=64, verbose=0)
test_loss, test_acc = model.evaluate(test_images, test_labels)
print("Accuracy: ", test_acc)

10000/10000 [==============================] - 2s 217us/step
Accuracy:  0.991599977016449

Convnets on small datasets

• Let's move to a more realistic dataset: Cats vs Dogs
  • We take a balanced subsample of 4000 real colored images
  • 2000 for training, 1000 validation, 1000 testing
• Convnets learn local patterns, which is highly efficient
• Translation invariant: a pattern can be recognized even if it is shifted to another part of the image
  • More robust, efficient to train (with fewer examples)
• We can use tricks such as data augmentation
• We can re-use pre-trained networks

Data preprocessing

• We use Keras' ImageDataGenerator to:
  • Decode JPEG images to floating-point tensors
  • Rescale pixel values to [0,1]
  • Resize images to 150x150 pixels
• Returns a Python generator we can endlessly query for images
  • Batches of 20 images per query
• Separately for training, validation, and test set

train_generator = train_datagen.flow_from_directory(
        train_dir, # Directory with images
        target_size=(150, 150), # Resize images 
        batch_size=20, # Return 20 images at a time
        class_mode='binary') # Binary labels

Build from scratch

model = models.Sequential()
model.add(layers.Conv2D(32, (3, 3), activation='relu',
                        input_shape=(150, 150, 3)))
model.add(layers.MaxPooling2D((2, 2)))
model.add(layers.Conv2D(64, (3, 3), activation='relu'))
model.add(layers.MaxPooling2D((2, 2)))
model.add(layers.Conv2D(128, (3, 3), activation='relu'))
model.add(layers.MaxPooling2D((2, 2)))
model.add(layers.Conv2D(128, (3, 3), activation='relu'))
model.add(layers.MaxPooling2D((2, 2)))
model.add(layers.Flatten())
model.add(layers.Dense(512, activation='relu'))
model.add(layers.Dense(1, activation='sigmoid'))

model.summary()

Model: "sequential_3"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
conv2d_7 (Conv2D)            (None, 148, 148, 32)      896       
_________________________________________________________________
max_pooling2d_3 (MaxPooling2 (None, 74, 74, 32)        0         
_________________________________________________________________
conv2d_8 (Conv2D)            (None, 72, 72, 64)        18496     
_________________________________________________________________
max_pooling2d_4 (MaxPooling2 (None, 36, 36, 64)        0         
_________________________________________________________________
conv2d_9 (Conv2D)            (None, 34, 34, 128)       73856     
_________________________________________________________________
max_pooling2d_5 (MaxPooling2 (None, 17, 17, 128)       0         
_________________________________________________________________
conv2d_10 (Conv2D)           (None, 15, 15, 128)       147584    
_________________________________________________________________
max_pooling2d_6 (MaxPooling2 (None, 7, 7, 128)         0         
_________________________________________________________________
flatten_2 (Flatten)          (None, 6272)              0         
_________________________________________________________________
dense_3 (Dense)              (None, 512)               3211776   
_________________________________________________________________
dense_4 (Dense)              (None, 1)                 513       
=================================================================
Total params: 3,453,121
Trainable params: 3,453,121
Non-trainable params: 0
_________________________________________________________________

Training

• Since the data comes from a generator, we use fit_generator
  • 100 steps per epoch (of 20 images each), for 30 epochs
  • Also provide sa generator for the validation data

model.compile(loss='binary_crossentropy',
              optimizer=optimizers.RMSprop(lr=1e-4),
              metrics=['acc'])
history = model.fit_generator(
      train_generator, steps_per_epoch=100,
      epochs=30, verbose=0,
      validation_data=validation_generator,
      validation_steps=50)

• Training takes more than an hour (on CPU)
• We save the trained model (and history) to disk so that we can reload it later

model.save(os.path.join(model_dir, 'cats_and_dogs_small_1.h5'))
with open(os.path.join(model_dir, 'cats_and_dogs_small_1_history.p'), 'wb') as file_pi:
    pickle.dump(history.history, file_pi)

Our model is overfitting: we need more training examples, more regularization

history = pickle.load(open("cats_and_dogs_small_1_history.p", "rb"))

acc = history.history['accuracy']
val_acc = history.history['val_accuracy']
loss = history.history['loss']
val_loss = history.history['val_loss']

epochs = range(len(acc))

plt.plot(epochs, acc, 'bo', label='Training acc')
plt.plot(epochs, val_acc, 'b', label='Validation acc')
plt.title('Training and validation accuracy')
plt.legend()

plt.figure()

plt.plot(epochs, loss, 'bo', label='Training loss')
plt.plot(epochs, val_loss, 'b', label='Validation loss')
plt.title('Training and validation loss')
plt.legend()

plt.show()

Data augmentation

• Generate new images via image transformations
  • Rotation, translation, shear, zoom, horizontal flip,...
• Keras has a tool for this:

datagen = ImageDataGenerator(
      rotation_range=40, width_shift_range=0.2,
      height_shift_range=0.2, shear_range=0.2,
      zoom_range=0.2, horizontal_flip=True,
      fill_mode='nearest')

Example

# This is module with image preprocessing utilities
from keras.preprocessing import image
plt.rcParams['figure.dpi'] = 120

train_cats_dir = os.path.join(base_dir, 'train', 'cats')
fnames = [os.path.join(train_cats_dir, fname) for fname in os.listdir(train_cats_dir)]

# We pick one image to "augment"
img_path = fnames[5]

# Read the image and resize it
img = image.load_img(img_path, target_size=(150, 150))

# Convert it to a Numpy array with shape (150, 150, 3)
x = image.img_to_array(img)

# Reshape it to (1, 150, 150, 3)
x = x.reshape((1,) + x.shape)

# The .flow() command below generates batches of randomly transformed images.
# It will loop indefinitely, so we need to `break` the loop at some point!
for a in range(2):
    i = 0
    for batch in datagen.flow(x, batch_size=1):
        plt.subplot(141+i) 
        plt.xticks([]) 
        plt.yticks([])
        imgplot = plt.imshow(image.array_to_img(batch[0]))
        i += 1
        if i % 4 == 0:
            break
        
    plt.tight_layout()
    plt.show()

We also add Dropout before the Dense layer

model = models.Sequential()
model.add(layers.Conv2D(32, (3, 3), activation='relu',
                        input_shape=(150, 150, 3)))
model.add(layers.MaxPooling2D((2, 2)))
model.add(layers.Conv2D(64, (3, 3), activation='relu'))
model.add(layers.MaxPooling2D((2, 2)))
model.add(layers.Conv2D(128, (3, 3), activation='relu'))
model.add(layers.MaxPooling2D((2, 2)))
model.add(layers.Conv2D(128, (3, 3), activation='relu'))
model.add(layers.MaxPooling2D((2, 2)))
model.add(layers.Flatten())
model.add(layers.Dropout(0.5))
model.add(layers.Dense(512, activation='relu'))
model.add(layers.Dense(1, activation='sigmoid'))

(Almost) no more overfitting!

history = pickle.load(open("cats_and_dogs_small_2_history.p", "rb"))

acc = history.history['acc']
val_acc = history.history['val_acc']
loss = history.history['loss']
val_loss = history.history['val_loss']

epochs = range(len(acc))

plt.plot(epochs, acc, 'bo', label='Training acc')
plt.plot(epochs, val_acc, 'b', label='Validation acc')
plt.title('Training and validation accuracy')
plt.legend()

plt.figure()

plt.plot(epochs, loss, 'bo', label='Training loss')
plt.plot(epochs, val_loss, 'b', label='Validation loss')
plt.title('Training and validation loss')
plt.legend()

plt.show()

Visualizing the intermediate outputs

• Let's see what the convnet is learning exactly by observing the intermediate feature maps
  • A layer's output is also called its activation
• Since our feature maps have depth 32/64/128, we need to visualize all
• We choose a specific input image, and observe the outputs

img_path = os.path.join(base_dir, 'test/cats/cat.1700.jpg')

# We preprocess the image into a 4D tensor
from keras.preprocessing import image
import numpy as np

img = image.load_img(img_path, target_size=(150, 150))
img_tensor = image.img_to_array(img)
img_tensor = np.expand_dims(img_tensor, axis=0) 
# Remember that the model was trained on inputs
# that were preprocessed in the following way:
img_tensor /= 255.

plt.imshow(img_tensor[0])
plt.show()

• We create a new model that is composed of the first 8 layers (the convolutional part)
• We input our example image and read the output

layer_outputs = [layer.output for layer in model.layers[:8]]
activation_model = models.Model(inputs=model.input, outputs=layer_outputs)
activations = activation_model.predict(img_tensor)

Output of the first Conv2D layer, 4th channel (filter):

• Similar to a diagonal edge detector
• Your own channels may look different

plt.rcParams['figure.dpi'] = 120
first_layer_activation = activations[0]

plt.matshow(first_layer_activation[0, :, :, 3], cmap='viridis')
plt.show()

Output of the 22th channel (filter):

• Cat eye detector?

plt.matshow(first_layer_activation[0, :, :,22], cmap='viridis')
plt.show()

• First 2 convolutional layers: various edge detectors

plot_activations(0,1)
plot_activations(2,3)

• 3rd convolutional layer: increasingly abstract: ears, eyes

plot_activations(4,5)

• Last convolutional layer: increasing sparsity. The learned patterns don't exist in the training data

plot_activations(6,7)

Spacial hierarchies

• Deep convnets can learn spacial hierarchies of patterns
  • First layer can learn very local patterns (e.g. edges)
  • Second layer can learn specific combinations of patterns
  • Every layer can learn increasingly complex abstractions

Visualizing the learned filters

• The filters themselves can be visualized by finding the input image that they are maximally responsive to
• gradient ascent in input space: start from a blank image, use loss to update the pixel values to values that the filter responds to more strongly

from keras import backend as K
    input_img = np.random.random((1, size, size, 3)) * 20 + 128.
    loss = K.mean(layer_output[:, :, :, filter_index])
    grads = K.gradients(loss, model.input)[0] # Compute gradient
    for i in range(40): # Run gradient ascent for 40 steps
        loss_v, grads_v = K.function([input_img], [loss, grads])
        input_img_data += grads_v * step

Let's do this for the VGG16 network pretrained on ImageNet

model = VGG16(weights='imagenet', include_top=False)

# VGG16 model
model.summary()

Model: "vgg16"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
input_1 (InputLayer)         (None, None, None, 3)     0         
_________________________________________________________________
block1_conv1 (Conv2D)        (None, None, None, 64)    1792      
_________________________________________________________________
block1_conv2 (Conv2D)        (None, None, None, 64)    36928     
_________________________________________________________________
block1_pool (MaxPooling2D)   (None, None, None, 64)    0         
_________________________________________________________________
block2_conv1 (Conv2D)        (None, None, None, 128)   73856     
_________________________________________________________________
block2_conv2 (Conv2D)        (None, None, None, 128)   147584    
_________________________________________________________________
block2_pool (MaxPooling2D)   (None, None, None, 128)   0         
_________________________________________________________________
block3_conv1 (Conv2D)        (None, None, None, 256)   295168    
_________________________________________________________________
block3_conv2 (Conv2D)        (None, None, None, 256)   590080    
_________________________________________________________________
block3_conv3 (Conv2D)        (None, None, None, 256)   590080    
_________________________________________________________________
block3_pool (MaxPooling2D)   (None, None, None, 256)   0         
_________________________________________________________________
block4_conv1 (Conv2D)        (None, None, None, 512)   1180160   
_________________________________________________________________
block4_conv2 (Conv2D)        (None, None, None, 512)   2359808   
_________________________________________________________________
block4_conv3 (Conv2D)        (None, None, None, 512)   2359808   
_________________________________________________________________
block4_pool (MaxPooling2D)   (None, None, None, 512)   0         
_________________________________________________________________
block5_conv1 (Conv2D)        (None, None, None, 512)   2359808   
_________________________________________________________________
block5_conv2 (Conv2D)        (None, None, None, 512)   2359808   
_________________________________________________________________
block5_conv3 (Conv2D)        (None, None, None, 512)   2359808   
_________________________________________________________________
block5_pool (MaxPooling2D)   (None, None, None, 512)   0         
=================================================================
Total params: 14,714,688
Trainable params: 14,714,688
Non-trainable params: 0
_________________________________________________________________

• Visualize convolution filters 0-2 from layer 5 of the VGG network trained on ImageNet

for i in range(3):
    plt.subplot(131+i) 
    plt.xticks([]) 
    plt.yticks([])
    plt.imshow(generate_pattern('block3_conv1', i))
plt.tight_layout()
plt.show();

First 64 filters for 1st convolutional layer in block 1: simple edges and colors

plt.rcParams['figure.dpi'] = 60
visualize_filter('block1_conv1')

Filters in 2nd block of convolution layers: simple textures (combined edges and colors)

visualize_filter('block2_conv1')

Filters in 3rd block of convolution layers: more natural textures

visualize_filter('block3_conv1')

Filters in 4th block of convolution layers: feathers, eyes, leaves,...

visualize_filter('block4_conv1')

Using pretrained networks

• We can re-use pretrained networks instead of training from scratch
• Learned features can be a generic model of the visual world
• Use convolutional base to contruct features, then train any classifier on new data

• Let's instantiate the VGG16 model (without the dense layers)
• Final feature map has shape (4, 4, 512)

  conv_base = VGG16(weights='imagenet', include_top=False, input_shape=(150, 150, 3))
  

conv_base.summary()

Model: "vgg16"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
input_2 (InputLayer)         (None, 150, 150, 3)       0         
_________________________________________________________________
block1_conv1 (Conv2D)        (None, 150, 150, 64)      1792      
_________________________________________________________________
block1_conv2 (Conv2D)        (None, 150, 150, 64)      36928     
_________________________________________________________________
block1_pool (MaxPooling2D)   (None, 75, 75, 64)        0         
_________________________________________________________________
block2_conv1 (Conv2D)        (None, 75, 75, 128)       73856     
_________________________________________________________________
block2_conv2 (Conv2D)        (None, 75, 75, 128)       147584    
_________________________________________________________________
block2_pool (MaxPooling2D)   (None, 37, 37, 128)       0         
_________________________________________________________________
block3_conv1 (Conv2D)        (None, 37, 37, 256)       295168    
_________________________________________________________________
block3_conv2 (Conv2D)        (None, 37, 37, 256)       590080    
_________________________________________________________________
block3_conv3 (Conv2D)        (None, 37, 37, 256)       590080    
_________________________________________________________________
block3_pool (MaxPooling2D)   (None, 18, 18, 256)       0         
_________________________________________________________________
block4_conv1 (Conv2D)        (None, 18, 18, 512)       1180160   
_________________________________________________________________
block4_conv2 (Conv2D)        (None, 18, 18, 512)       2359808   
_________________________________________________________________
block4_conv3 (Conv2D)        (None, 18, 18, 512)       2359808   
_________________________________________________________________
block4_pool (MaxPooling2D)   (None, 9, 9, 512)         0         
_________________________________________________________________
block5_conv1 (Conv2D)        (None, 9, 9, 512)         2359808   
_________________________________________________________________
block5_conv2 (Conv2D)        (None, 9, 9, 512)         2359808   
_________________________________________________________________
block5_conv3 (Conv2D)        (None, 9, 9, 512)         2359808   
_________________________________________________________________
block5_pool (MaxPooling2D)   (None, 4, 4, 512)         0         
=================================================================
Total params: 14,714,688
Trainable params: 14,714,688
Non-trainable params: 0
_________________________________________________________________

Using pre-trained networks: 3 ways

• Fast feature extraction without data augmentation
  • Call predict from the convolutional base
  • Use results to train a dense neural net
• Feature extraction with data augmentation
  • Extend the convolutional base model with a Dense layer
  • Run it end to end on the new data (expensive!)
• Fine-tuning
  • Do any of the above two to train a classifier
  • Unfreeze a few of the top convolutional layers
    • Updates only the more abstract representations
  • Jointly train all layers on the new data

Fast feature extraction without data augmentation

• Extract filtered images and their labels
  • You can use a data generator again

generator = datagen.flow_from_directory(dir, target_size=(150, 150),
        batch_size=batch_size, class_mode='binary')
for inputs_batch, labels_batch in generator:
    features_batch = conv_base.predict(inputs_batch)

• Build Dense neural net (with Dropout)
• Train and evaluate with the transformed examples

model = models.Sequential()
model.add(layers.Dense(256, activation='relu', input_dim=4 * 4 * 512))
model.add(layers.Dropout(0.5))
model.add(layers.Dense(1, activation='sigmoid'))

• Validation accuracy around 90%, much better!
• Still overfitting, despite the Dropout: not enough training data

import matplotlib.pyplot as plt

acc = history.history['acc']
val_acc = history.history['val_acc']
loss = history.history['loss']
val_loss = history.history['val_loss']

epochs = range(len(acc))

plt.plot(epochs, acc, 'bo', label='Training acc')
plt.plot(epochs, val_acc, 'b', label='Validation acc')
plt.title('Training and validation accuracy')
plt.legend()

plt.figure()

plt.plot(epochs, loss, 'bo', label='Training loss')
plt.plot(epochs, val_loss, 'b', label='Validation loss')
plt.title('Training and validation loss')
plt.legend()

plt.show()

Feature extraction with data augmentation

• Use data augmentation to get more training data
• Simply add the Dense layers to the convolutional base
• Freeze the convolutional base (before you compile)

model = models.Sequential()
model.add(conv_base)
model.add(layers.Flatten())
model.add(layers.Dense(256, activation='relu'))
model.add(layers.Dense(1, activation='sigmoid'))
conv_base.trainable = False

model.summary()

Model: "sequential_7"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
vgg16 (Model)                (None, 4, 4, 512)         14714688  
_________________________________________________________________
flatten_4 (Flatten)          (None, 8192)              0         
_________________________________________________________________
dense_9 (Dense)              (None, 256)               2097408   
_________________________________________________________________
dense_10 (Dense)             (None, 1)                 257       
=================================================================
Total params: 16,812,353
Trainable params: 2,097,665
Non-trainable params: 14,714,688
_________________________________________________________________

Data augmentation and training (takes a LONG time)

train_datagen = ImageDataGenerator(
      rescale=1./255, rotation_range=40, width_shift_range=0.2,
      height_shift_range=0.2, shear_range=0.2, zoom_range=0.2,
      horizontal_flip=True, fill_mode='nearest')
train_generator = train_datagen.flow_from_directory(dir,
      target_size=(150, 150), batch_size=20, class_mode='binary')
history = model.fit_generator(
      train_generator, steps_per_epoch=100, epochs=30,
      validation_data=validation_generator, validation_steps=50)
model.save(os.path.join(model_dir, 'cats_and_dogs_small_3.h5'))
with open(os.path.join(model_dir, 'cats_and_dogs_small_3_history.p'), 'wb') as file_pi:
    pickle.dump(history.history, file_pi)

We now get about 96% accuracy, and very little overfitting

Fine-tuning

• Add your custom network on top of an already trained base network.
• Freeze the base network.
• Train the part you added.
• Unfreeze some layers in the base network.
• Jointly train both these layers and the part you added.

for layer in conv_base.layers:
    if layer.name == 'block5_conv1':
        set_trainable = True
    else:
        layer.trainable = False

Visualized

• Load trained network, finetune
  • Use a small learning rate, large number of epochs
  • You don't want to unlearn too much

model = load_model(os.path.join(model_dir, 'cats_and_dogs_small_3.h5'))
model.compile(loss='binary_crossentropy', 
              optimizer=optimizers.RMSprop(lr=1e-5),
              metrics=['acc'])
history = model.fit_generator(
      train_generator, steps_per_epoch=100, epochs=100,
      validation_data=validation_generator,
      validation_steps=50)

• Learning curves are a bit noisy, smooth them using a running average

def smooth_curve(points, factor=0.8):
  smoothed = []
  for point in points:
    if smoothed:
      previous = smoothed[-1]
      smoothed.append(previous * factor + point * (1 - factor))
    else:
      smoothed.append(point)
  return smoothed

• Results: 97% accuracy (1% better)
• Better validation accuracy, worse validation loss

Visualizing class activation

• We can also visualize which part of the input image had the greatest influence on the final classification
  • Helpful for interpreting what is learned (or misclassified)
• Class activation maps: produce heatmap over the input image
  • Take the output feature map of a convolution layer
  • Weigh every channel (filter) by the gradient of the class with respect to the channel
• Find important channels, see what activates those

• Try VGG (including the dense layers) and an image from ImageNet

  model = VGG16(weights='imagenet')
  

  

• Load image
• Resize to 224 x 224 (what VGG was trained on)
• Do the same preprocessing (Keras VGG utility)

from keras.applications.vgg16 import preprocess_input
img_path = '../images/10_elephants.jpg'
img = image.load_img(img_path, target_size=(224, 224))
x = image.img_to_array(img)
x = np.expand_dims(x, axis=0) # Transform to batch of size (1, 224, 224, 3)
x = preprocess_input(x)

• Sanity test: do we get the right prediction?

preds = model.predict(x)

preds = model.predict(x)
print('Predicted:', decode_predictions(preds, top=3)[0])

Predicted: [('n02504458', 'African_elephant', 0.909421), ('n01871265', 'tusker', 0.086182885), ('n02504013', 'Indian_elephant', 0.0043545826)]

Visualize the class activation map

heatmap = np.maximum(heatmap, 0)
heatmap /= np.max(heatmap)
plt.matshow(heatmap)
plt.show()

• Superimpose on our image

One more thing: Batch Normalization

• Normalization (in general) aims to make different examples more similar to each other
  • Easier to learn and generalize
• Standardization (centering the data to 0 and scaling to 1 stddev)
  • This assumes that the data is normalliy distributed
• Batch normalization layer adaptively normalize data, even as the mean and variance change over time during training.
  • It works by internally maintaining an exponential moving average of the batch-wise mean and variance of training data
  • Helps with gradient propagation, allows for deeper networks.

BatchNormalization layer is typically used after a convolutional or densely connected layer:

conv_model.add(layers.Conv2D(32, 3, activation='relu'))
conv_model.add(layers.BatchNormalization())

dense_model.add(layers.Dense(32, activation='relu')) 
dense_model.add(layers.BatchNormalization())

Take-aways

• Convnets are ideal for attacking visual-classification problems.
• They learn a hierarchy of modular patterns and concepts to represent the visual world.
• Representations are easy to inspect
• Data augmentation helps fight overfitting
• Batch normalization helps train deeper networks
• You can use a pretrained convnet to do feature extraction and fine-tuning